I'm probably less knowledgeable on this than others on this thread [1].
The best answer is that all of them are true. Newton & conservation of momentum is a basic law. The wing does push the air down, hence the air pushes the wing up. A planar wing would deflect air downward and provide lift.
The way I've always thought of Bernoulli is that it enhances / increases the "Newtonian" air deflecton. The curvature changes the pressure on the wing, gives an even lower pressure on the top and higher on the bottom than the planar wing would get. So the wing pushes the air down harder than a flat plane would, so gets a bigger Newtonian push up.
This gives a way to think about flying inverted... the same basic air deflection is happening, just less efficiently because the Bernoulli effect is worked against the lift rather than for it.
I think the confusion is that some textbooks describe some percent of lift as from Bernoulli and some from deflecting air. It is really all from deflecting air, just that some is deflected because of the basic planar shape, some increased amount because of the curve.
[1] But sadly, to everyone's disappointment, that won't keep me from posting. 